what is the value
`frac{a+b omega+c omega^(2)}{c+a omega+b omega^(2)}` + `frac{a+b omega+c omega^(2)}{b+c omega+a omega^(2)}`

Prove the following (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) + (a + b omega + c omega^(2))/(b + c omega + a omega^(2)) = -1

Prove the following (1- omega + omega^(2)) (1 + omega- omega^(2)) (1 - omega- omega^(2))= 8

Prove the following (a + b omega + c omega^(2))/(b + c omega + a omega^(2))= omega

If omega and omega^(2) are cube roots of unity, prove that (2- omega + 2omega^(2)) (2 + 2omega- omega^(2))= 9

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega - omega^(2)) (1- omega + omega^(2))=4

If 1, omega and omega^(2) are the cube roots of unity, prove that (a+b omega+c omega^(2))/(c+a omega+b omega^(2))=omega^(2)

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

The value of (a+bomega+comega^2)/(b+comega+aomega^2)+(a+bomega+comega^2)/(c+aomega+bomega^2) (where 'omega' is the imaginary cube root of unity), is (a) -omega (b). omega^2 (c). 1 (d). -1

If omega is an imaginary cube root of unity, then the value of the determinant |(1+omega,omega^2,-omega),(1+omega^2,omega,-omega^2),(omega+omega^2,omega,-omega^2)|

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is